It never fails: I always have a student who is absent on the day I discuss trig proofs. The next day they watch us do the warm-up and go over the homework and are completely baffled. So I created a step-by-step guide on a few proofs with detailed reasoning. The students start by looking at graphs of a few identities and deciding which are equal. I then walk them through two proofs and ask them to fill out the reasoning of a third proof. The sample shows half of the first proof.
In order for this to work with your classes, your students need to know the reciprocal, quotient, and Pythagorean Identities and how to enter the reciprocal functions in their calculator [example: cosecant is entered as 1/sin(x)]. I hope you find this resource useful.
Document is editable.